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Questions tagged [natural-proofs]

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2
votes
1answer
74 views

Validity of a modal argument about “vagueness”

(2nd version to make explicit my implicit assumptions about A, B and C, and the definitions of the non-logical constants "⊂" and "≡".) Intuitively, the following modal argument seems valid to me and ...
5
votes
0answers
158 views

Converse to natural proofs theorem?

Natural proofs paper shows 'if there is a natural property not possessed by any function in P/poly then there is no $2^{n^\epsilon}$-hard PRG'. Is it easy to see the converse 'if there is no $2^{n^\...
4
votes
0answers
87 views

Sampling Functions Efficiently vs Pseudorandom Generators

Let $X$ be a set of $n$-bit Boolean functions of the form $f:\{0,1\}^n\rightarrow \{0,1\}$. For instance, $X$ could be the set of $n$-bit monotone Boolean functions, or the set of $n$-bit functions ...
15
votes
0answers
447 views

Williams' Method, Natural Proofs and Constructivity

I have some questions on the previous question which is written bellow. Natural Proof and Constructivity : The topic of the previous question Recently, Ryan Williams proved that Constructivity in ...
11
votes
0answers
500 views

Has there been any result which does not have any Natural Proofs?

Alexander Razborov and Steven Rudich's Natural Proofs result is one of the major barriers against proving circuit lower bounds. The paper is almost 20 years old (it was published in 1994). Has there ...
13
votes
0answers
285 views

Pseudorandom functions in ACC^0?

In the lower bound result by Ryan Williams (Non-uniform $\mathsf{ACC}$ circuit lower bounds), there is a mention of "little evidence that Pseudorandom function generators exist in $\mathsf{ACC}^0$. Is ...
28
votes
1answer
1k views

Toy examples for barriers to $P \ne NP$

Are there any toy examples that provide 'essential' insights into understanding the three known barriers to $P = NP$ problem - relativization, natural proofs and algebrization?
18
votes
2answers
1k views

Hierarchy theorem for circuit size

I think that a size hierarchy theorem for circuit complexity can be a major breakthrough in the area. Is it an interesting approach to class separation? The motivation for the question is that we ...
0
votes
1answer
198 views

quasiP-Natural Property again SIZE($n^e$) for fixed e.

The Natural Proof theorem says : If for a fixed $c>1$ $G_k \in SIZE(k^c)$ is $2^{k^\epsilon}$-hard then not exists a $quasiP$-Natural Property that for all $e$ sufficently large is usefull against ...
6
votes
0answers
165 views

Distributions over circuits and N-to-N vs N-to-1 circuits

This is really a two part question, and they aren't necessarily related. First, my understanding of natural proof barriers is that they are based on the idea that a suitable distribution over small ...
15
votes
1answer
687 views

Random monotone function

In Razborov-Rudich's Natural Proofs paper, page 6, in the part they discuss that there are "strong lowerbounds proofs against monotone circuit models" and how they fit into the picture, there are the ...
15
votes
2answers
890 views

Barriers and Monotone Circuit Complexity

Natural proofs is a barrier towards proving lower bounds on the circuit complexity of boolean functions. They do not directly imply any such barrier in proving lower bounds on the $monotone$ circuit ...